Puree the mustard and egg in a blender on low speed until completely combined. With the motor running, slowly drizzle in the oil until the mixture is thick and smooth. Add the cashew milk, lemon juice, dried onion, garlic, 1 teaspoon salt and 1/4 teaspoon pepper and puree until combined. Transfer to a small bowl or serving pitcher and stir in the chives and dill.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.
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